A290473 Numbers k such that 3*10^k + 13 is prime.

1, 2, 4, 10, 12, 13, 26, 37, 56, 66, 288, 404, 3495, 3824, 7780, 14824, 17928, 18680, 21414, 23782, 25392, 34749, 36180, 46316, 48477, 63522, 73962, 89206, 139722, 172812, 184110

Offset

1,2

Comments

For k>1, numbers such that the digit 3 followed by k-2 occurrences of the digit 0 followed by the digits 13 is prime (see Example section).

a(32) > 2*10^5.

Links

Table of n, a(n) for n=1..31.

Makoto Kamada, Factorization of near-repdigit-related numbers.

Makoto Kamada, Search for 30w13.

Example

4 is in this sequence because 3*10^4 + 13 = 30013 is prime.
Initial terms and primes associated:
a(1) = 1, 43;
a(2) = 2, 313;
a(3) = 4, 30013;
a(4) = 10; 30000000013;
a(5) = 12, 3000000000013; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[3*10^# + 13] &]

Prog

(PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(3*10^n + 13), print1(n, ", "))); \\ Altug Alkan, Aug 03 2017

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Sequence in context: A227204 A249446 A184815 * A356664 A138940 A278465

Adjacent sequences: A290470 A290471 A290472 * A290474 A290475 A290476

Keyword

nonn,more,hard

Author

Robert Price, Aug 03 2017

Extensions

a(29)-a(31) from Robert Price, Jul 26 2018

Status

approved